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Grade 5 Mathematics Diagnostic

NC EOG-Aligned Readiness Assessment

📚 Mathematics 🎓 Grade 5 ⏱️ 60 minutes

Learning Objectives

  • Write, evaluate, and interpret numerical expressions and analyze numerical patterns.

  • Explain the base-ten place value system and read, write, and compare decimals to thousandths.

  • Multiply and divide multi-digit whole numbers and compute with decimals.

  • Add and subtract fractions and mixed numbers with unlike denominators.

  • Multiply and divide fractions and interpret fractions as division.

  • Convert measurement units, interpret data displays, and find volume.

  • Graph points in the first quadrant and classify quadrilaterals.

Progress 6 sections
1

Directions

~3 minutes

This diagnostic checks your readiness across all five Grade 5 math domains. It mirrors the emphasis of the NC End-of-Grade test, so most questions focus on fractions and decimals. Work carefully and show your thinking on scratch paper.

2

Operations & Algebraic Thinking

~8 minutes

Two number patterns. Pattern A starts at 0 and adds 3. Pattern B starts at 0 and adds 9.

StepPattern APattern B
100
239
3618
| 4 | 9 | 27 |

Question 1

Evaluate the expression: $3 \times (12 - 4) + 6 \div 2$

Question 2

Maria buys 4 packs of pencils with 6 pencils in each pack, then gives away 5 pencils. Which expression shows how many pencils she has left?

Question 3

Use the table shown. Each Pattern B value is how many times the matching Pattern A value?

3

Number & Operations in Base Ten

~14 minutes
Question 4

In the number 4.836, what is the value of the digit 3?

Question 5

The value of the 7 in 2,700 is how many times the value of the 7 in 270?

Question 6

Which comparison is true?

Question 7

Write $3 + 0.4 + 0.05 + 0.007$ in standard form.

Question 8

What is the product of $36 \times 47$?

Question 9

What is $1{,}288 \div 23$?

Question 10

Find $12.5 - 3.74$.

Question 11

Multiply $0.6 \times 0.4$.

4

Number & Operations - Fractions

~20 minutes
Area model for 2/3 x 3/4
A 3-by-4 grid (12 cells). Two of three columns and three of four rows overlap, shading 6 of the 12 cells to model two-thirds times three-fourths equaling six-twelfths....
Number line for 4 divided by one-half
A number line from 0 to 4 marked in halves. Eight equal half-unit jumps span from 0 to 4, showing that 4 divided by one-half equals 8....
Question 12

Add $\frac{1}{2} + \frac{1}{3}$.

Question 13

Subtract $\frac{3}{4} - \frac{1}{8}$.

Question 14

Add the mixed numbers $2 \frac{1}{2} + 1 \frac{3}{4}$.

Question 15

A recipe needs $\frac{2}{3}$ cup of white sugar and $\frac{1}{4}$ cup of brown sugar. How much sugar is needed in all?

Question 16

Which expression has the same value as $3 \div 5$?

Question 17

Four friends share 3 sandwiches equally. How much sandwich does each friend get?

Question 18

Use the area model shown. What is $\frac{2}{3} \times \frac{3}{4}$?

Question 19

What is $\frac{3}{4} \times 8$?

Question 20

Without multiplying, decide: the product $7 \times \frac{3}{5}$ is ___ 7.

Question 21

Divide $\frac{1}{3} \div 2$.

Question 22

Use the number line shown. What is $4 \div (\frac{1}{2})$?

Question 23

Which is the best estimate for $\frac{7}{8} + \frac{11}{12}$?

5

Measurement & Data

~8 minutes
Line plot of plant heights
A line plot of plant heights in inches. Above 1 inch there are 2 dots, above 2 inches 3 dots, above 3 inches 5 dots, above 4 inches 3 dots, and above 5 inches 1 dot....
Rectangular prism 6 by 2 by 4
A rectangular prism (box) labeled 6 centimeters long, 2 centimeters wide, and 4 centimeters tall....
Question 24

A conversion chart shows 1 foot = 12 inches. How many inches are in 5 feet?

Question 25

Use the line plot shown. How many plants are 3 inches or taller?

Question 26

Use the prism shown (6 cm by 2 cm by 4 cm). What is its volume?

Question 27

A storage box is filled with 1-centimeter cubes. It is 5 cubes long, 3 cubes wide, and 2 cubes tall. How many cubes fill the box?

6

Geometry

~7 minutes
Point P on a coordinate grid
A first-quadrant coordinate grid from 0 to 8 on both axes with point P plotted at 3 right and 5 up, that is at coordinates (3, 5)....
Question 28

Use the grid shown. What ordered pair locates point P?

Question 29

A robot starts at (2, 1). It moves 3 units right and 2 units up. Where does it land?

Question 30

Match each quadrilateral with the property that best describes it.

Square
Rhombus
Trapezoid
Rectangle